Wave loads on breakwaters, seawalls, and other marine structures
Transcript of Wave loads on breakwaters, seawalls, and other marine structures
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H. Oumeraci, E-mail: [email protected]ß-Institute for Hydromechanics and Coastal Engineering, Technical University Braunschweig, BraunschweigCoastal Research Centre, University Hannover and Technical University Braunschweig, Hannover
Wave Loads on Breakwaters, Sea-Walls and other Marine StructuresWave Loads on Breakwaters, Sea-Walls and other Marine Structures
FZK
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Introduction
Main Experimental Facilities and Expertise
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Leichtweiss-Institute for Hydraulic EngineeringLeichtweiss-Institute for Hydraulic Engineering
Hydromechanics & Coastal Engineering
Homepage: http://www.LWI.tu-bs.de
Technical University Braunschweig
Length ≈ 90m
2m 1m
Depth = 1,25m
WaveWave
(a) Plan view of twin-flume
b) Twin-Wave Paddle (Synchron or independent)
up to 30cm high solitary waves
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Coastal Research Centre (FZK) in HannoverCoastal Research Centre (FZK) in Hannover
Coastal Research Centre
FZKJoint Central Institution of
the University of Hannover and theTechnical University of Braunschweig
Large Wave Flume (GWK)
Homepage:http://www.hydrolab.de/
Dimensions
330m x 5m x 7m
up to 1m high solitary waves
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Pile
F
F
Seadikes and Revetments Rubble Mound Breakwaters Caisson-Breakwaters
Wave Absorber as a Sea Wall Wave Absorber as Artificial Reef Innovative Sea Walls
Beach Profile Development underStorm Surge Conditions
Dune Stability and Reinforcementwith Geotextile Constructions
Wave Impact Loading& Scour (in progress)
SWL
Investigated Coastal Marine Structure (Selected)Investigated Coastal Marine Structure (Selected)
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Waves & Water Levels(at Structure)
Wave Refelction
IncidentWaves
(Farfield)
Waves & Water Levels(Nearfields)
StructureLoad
Wave Transmission
StructureLoad
Structure- and Soil Parameters
Structureresponse
Wave Overtopping
Structure Response Wave Transmission
Structure Parameters
Indirect Loadingof Foundation Soil
Direct Loadingof Foundation SoilTF
TF
TF
TF
TF
TF
TF
TF TF
TF
TF
Sea Wave-Structure-Foundation InteractionSea Wave-Structure-Foundation Interaction
CoV ≥ 10%CoV ≥ 20%
CoV = Coefficient of VariationTF = Transfer function (Model)
CoV > 50%
CoV ≥ 20%
CoV > 30%
CoV > 20%CoV > 30%
CoV ≥ 15%
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Research StrategyResearch Strategy
Validated predictive formulae and graphs (empirical/semi-empirical)
Identify most essential and crucial features of processes to be predicted
Conceptual model (original idea/hypothesis)
Numerical modelling to supplement/support small scale
model study
Physical Modelling (small scale model tests for systematic
parameter study)
Qualitative (and partly quantitative) understanding of physical processes to be
investigated
and/or
Improved quantitative understanding of processes to be predicted
Ultimate Scientific Result:
Prototype observations and measurements (model and scale effects)
Qu
anti
tati
ve
adju
stm
ent
and
exte
nsi
on
Cor
rect
ion
fo
r sc
ale
and
mod
el e
ffec
ts
Verif
icat
ion
and
valid
atio
n
Verif
icat
ion
and
valid
atio
n
Processes observed in nature
Validated sophisticated numerical model used as a research predictive tool
Large-scale model tests (scale effects)
Detailed conceptual model (generalized and validated)
Processes observed in nature
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1. Introduction
2. Wave Loads on Pile Structures
3. Wave Forces on Submerged Bodies
4. Wave Loads on Monolithic Breakwater and Sea Walls
OutlineOutline
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2. Wave Loads on Pile Structures (3D)
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2.1 Wave Load Classification
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Non Slender and Slender StructuresNon Slender and Slender Structures
L
C
Hi Ht
Ht≠Hi
D
FH
FV
D > 0.05LNon Slender Structures(Diffraction + Reflection)
π⋅D/L= Diffraction parameter
(a)
Incident Wave
L
C
Hi Ht
Ht=Hi
D
FH
D < 0.05LSlender Structures
(Hydraulically transparent)
(b)
Incident Wave
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Relative Importance of Drag and Inertia Forces FD and FMRelative Importance of Drag and Inertia Forces FD and FM
D> (1/16.h/L)HD ≥ 0,2H
(1/100.h/L)H<D<
(1/16.h/L)H
(H/32)<D<(H/5)
D< (1/100.h/L)HD≤ (H/32)
Transition & Shallowwater
(h/L < 0,5)
Deep water(h/L ≥ 0,5)
D= H(1
6. h/L
)
Drag forces dominate for smaller D and larger wave
heights H
Inertia forces dominate for larger D and smaller wave
heights H
Transtion Deep waterShallow water
D= H(100.h/L)
0,1
0,025
0,2
1
2
100,01 1,00,1
h/L
D/H
MORISON-Formula:
FTot = FM
FTot = FM + FD
FTot = FD
Total Force FTot
hπ⋅ ∂
= ⋅ρ ⋅ ⋅ ⋅ + ⋅ρ ⋅ ⋅∂
2
ges D w m w
Drag component Inertiacomponent
1 D uf C D u u c
2 4 t
(Deep water)D= H/32
D= H/5 (Deep water)
Both Drag and Inertia are important
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Wave Load at Different LocationsWave Load at Different Locations
FH
FH (t)FH
generally quasi-static generally dynamic generally dynamic
Seawards of surf zoneNon breaking waves
Shorewards of surf zoneBroken waves (bores)
Surf zoneBreaking waves
Wave Load Classification
FH (t)
Seaward of shoreline
Landward of shoreline
enough knowledge available insufficient knowledge
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2.2 Breaking Wave Impact Load on Single Pile in Deeper Water
References:
• Wienke, J. (2001): Impact loading of slender pile structures induced by breaking waves in deeper water, PhD-Thesis, Leichtweiss-Institute, TU Braunschweig (in German)
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Extreme Loads Due to Breaking WavesExtreme Loads Due to Breaking Waves
PROTOTYPE GWK MODEL
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Breaking Wave Forces on Slender CylindersBreaking Wave Forces on Slender Cylinders
λ = „Curling Factor“
MWS
Breaking wave
Total force =
FTot = FM + FD + FI
C Fη‘
λ.η'
inertia/drag force (quasi-static force
impact force+
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Slamming Coefficient and Pile-up EffectsSlamming Coefficient and Pile-up Effects
no pile-uppile-up effect
CS(t=0)=πvon
Karman(1929)
CS(t=0)=2πWagner(1932)
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Theoretical Formulae for Slamming ForcesTheoretical Formulae for Slamming Forces
y
x
η
x R
c(t)
ηb V.t
f
V
pile-up effect
flat plate
• analytical solution by flat plate approximation
• experimentally verified by pressure measurement
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t / R/V0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
f/ ρ R
V2
0
π
2π
ignoring pile-up effect
new approach
Theoretical Formulae for Slamming ForcesTheoretical Formulae for Slamming Forces
y
xη
x Rf
V
Line force ρ= ⋅ ⋅ ⋅ 2maxf SC R V
= ⋅1332D
RTC
Slam
min
g Fa
ctor
Impact load duration:
C S=
with CS = Slamming Factor
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Loading Cases for Vertical Cylinder in GWKLoading Cases for Vertical Cylinder in GWK
Wave breaking behind pile
Wave breaking at pile
Wave breaking just in front of pile
Wave breaking in front of pile
Broken wave at pile
Bre
aker
Forc
e -
Tim
eV
ideo
SWL SWL SWL SWL SWL
Forc
e
TimeFo
rce
Time
Forc
e
Time
Forc
e
Time
Forc
e
Time
quasi-static
1. 2. 3. 4. 5.
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Loading Cases for Vertical Cylinder in GWKLoading Cases for Vertical Cylinder in GWK
Wave breaking behind pile
Wave breaking at pile
Wave breaking just in front of pile
Wave breaking in front of pile
Broken wave at pile
Bre
aker
Forc
e -
Tim
eV
ideo
SWL SWL SWL SWL SWL
Forc
e
TimeFo
rce
Time
Forc
e
Time
Forc
e
Time
Forc
e
Time
quasi-static
1. 2. 3. 4. 5.
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Loading Cases for Vertical Cylinder in GWKLoading Cases for Vertical Cylinder in GWK
Wave breaking behind pile
Wave breaking at pile
Wave breaking just in front of pile
Wave breaking in front of pile
Broken wave at pile
Bre
aker
Forc
e -
Tim
eV
ideo
SWL SWL SWL SWL SWL
Forc
e
TimeFo
rce
Time
Forc
e
Time
Forc
e
Time
Forc
e
Time
quasi-static
1. 2. 3. 4. 5.
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Loading Cases for Vertical Cylinder in GWKLoading Cases for Vertical Cylinder in GWK
Wave breaking behind pile
Wave breaking at pile
Wave breaking just in front of pile
Wave breaking in front of pile
Broken wave at pile
Bre
aker
Forc
e -
Tim
eV
ideo
SWL SWL SWL SWL SWL
Forc
e
TimeFo
rce
Time
Forc
e
Time
Forc
e
Time
Forc
e
Time
quasi-static
1. 2. 3. 4. 5.
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Loading Cases for Vertical Cylinder in GWKLoading Cases for Vertical Cylinder in GWK
Wave breaking behind pile
Wave breaking at pile
Wave breaking just in front of pile
Wave breaking in front of pile
Broken wave at pile
Bre
aker
Forc
e -
Tim
eV
ideo
SWL SWL SWL SWL SWL
Forc
e
TimeFo
rce
Time
Forc
e
Time
Forc
e
Time
Forc
e
Time
quasi-static
1. 2. 3. 4. 5.
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Loading Cases Investigated in GWK for Vertical & Inclined Cylinders (1)Loading Cases Investigated in GWK for Vertical & Inclined Cylinders (1)
-45° -25° 0° +24,5° +45°
1
2
3
4
5
quasi-static
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Loading Cases Investigated in GWK for Vertical & Inclined Cylinders (2)Loading Cases Investigated in GWK for Vertical & Inclined Cylinders (2)
quasi-static
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Loading Case 3 for Different Pile Inclination AnglesLoading Case 3 for Different Pile Inclination Angles
-45° Inclined against wave direction
-25° Inclined against wave direction
0° vertical pile
+24.5° Inclined in wave
direction
+45° Inclined in wave
direction
RWS
RWS
RWS
RWS
RWS
Loading Case 3
SWL SWL SWL SWL SWL
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Slamming Forces: Definition SketchSlamming Forces: Definition Sketch
time [s]
0,0 0,4 0,8 1,2 1.6
forc
e [k
N]
-20
0
20
40
60
t1
t2
FI
F0
TD
t0
F2
actualtotal force
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Impact Force for Loading Case 3 Different Pile InclinationsImpact Force for Loading Case 3 Different Pile Inclinations
t
F F1
( )π λ η ρ= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 21 2 'F R V
α [°]-45.0 -25.0 0.0 24.5 45.0
F1 [kN]
0
20
40
60
80max
min
mittel
Loading Case 3
SWL
mean
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Breaking Wave Impact on Slender Structures (Video)Breaking Wave Impact on Slender Structures (Video)
Breaker Heights up to 3.25m generated!
HB ≈ 2.8m just in Front of Cylinder
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Wave With Vertical Front at Cylinder and Splash GenerationWave With Vertical Front at Cylinder and Splash Generation
C
SplashSplash
C
wave crests
Wave withvertical front at
cylinder
V(z)
R
dz
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Breaking Wave Impact as a Radiation ProcessBreaking Wave Impact as a Radiation Process
C
Breakingwave at cylinder
Splash
C
wave crests
(a) Side View (b) Front View
Splash
SWL SWL
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Theoretical 3D-Model for Impact ForceTheoretical 3D-Model for Impact Force
F = FD + FM + FI
MorisonForce
Impact Force
For time: t = 0 : ÷1 R8 V cos γ
γ γ−
⎡ ⎤⎛ ⎞ ⎛ ⎞= ρ η γ π −⎢ ⎥⎜ ⎟ ⎜ ⎟
⎢ ⎥⎝ ⎠ ⎝λ
⎠⎣ ⎦l b
V cos 1 V cost 1 t
R 4 RF Rv² cos² 2 2 arctanh
For time t´ = , with t´ = t - :3 R32 V cos γ
÷ 12 R32 V cos γ
1 R32 V cos γ
−⎡ ⎤γ γ γ γ⎛ ⎞⎢ ⎥= ρ η γ π −λ −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
1
4l b
1 V cos 8 V cos V cos V cosF Rv² cos² t́ t́ arctanh 1 t́ 6 t́
6 R 3 R R R
Duration TD of Impact Force FI
=γD
13 RT
32 V cos, mit C(TD) = R
Wienke, J; Oumeraci, H (2005): Breaking wave impact on a vertical and inclined slender pile –theoretical and large-scale model investigation. Coastal Engineering. Elsevier vol. 52 pp 435-462.
• Adopted in ISO/CD 21650 “Actions from wave and currents” (in print)
• Adopted in New German Lloyd Guidelines (2005)
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λ = 0.46 für α = 0
„Curling Factor“ for Vertical and Inclined Cylinder„Curling Factor“ for Vertical and Inclined Cylinder
λ . ηb
R
C
SWL
Impact area
bh
Hb
α
C
VVγg.t α
C
V
β
( )CV cos
cos⊥ = ⋅ α − ββ
CV
cos=
β für α = -45° bis +45°und β ≈ -45°
( )coscos
α − βλ =
α
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Time Dependent Slamming Coefficient (Wienke and Oumeraci, 2005)Time Dependent Slamming Coefficient (Wienke and Oumeraci, 2005)
Wagner (1932)
Von Karman (1929)
Wienke (2001)
CS
= f
S/ρ
RV
²
Campbell & Weynberg(1979)
Campbell et al. (1977)Cointe (1989)
Goda et al. (1966)
Fabula(1957)
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2.3 Breaking Wave Impact Load on Single Pile in Shallow Water
References:
• Irschik, K. (2007): Impact loading of slender pile structures induced by depth limited breaking waves, PhD-Thesis, TU Braunschweig (in German)
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Breaking Wave Loads (Slamming Coefficient Approach)Breaking Wave Loads (Slamming Coefficient Approach)
= ρ Δ'T o t wD
1F (D
2C z ) u u
− ≈D,non breakingwith C 0,7= ≈ ≈b b
For shallow water :
u c gh gH
2bu u u gH= =
D
hb
Hb Δ = =Dz Impact height of f f(Breaktype) :
bz HΔ ≈
≈ ρ ⋅ ⋅ ⋅ 2Tot w bF 0,88 g D H
≈D, breakingC 1,75
−≈'D,breaking D non breakingC 2,5(C )
(FM≈0 ⇒ FTot≈ FD)
Problem: Response characteristics of structure not considered.
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Quasi-Static Force and Impact ForcesQuasi-Static Force and Impact Forces
( )= + +D M IF F F F
Non-breaking wave:
• quasi-static force
MD FFF +=MORISON equation
Breaking wave:
• quasi-static + impact force
MWL
C F
MWL
CFηb
λ . ηb
R
Cs: slamming coefficient
λ: curling factor
= ⋅ ⋅ ⋅ ⋅ ⋅⋅2 2cosI s bF R V C λ ηρ α
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Curling Factor for Depth Limited Wave BreakingCurling Factor for Depth Limited Wave Breaking
( )α⋅η⋅λ⋅⋅⋅⋅ρ=
++=2
bs2
I
IMD
cosCVRF
FFFF
Non-breaking wave:
• quasi-static force
MD FFF +=MORISON equation
Breaking wave:
• quasi-static + impact force
MWL
C F
MWL
CFηb
λ . ηb
R
Cs: slamming coefficient
λ: curling factor
Estimation of curling factor λ for depth limited breaking waves
PhD-Thesis of Mr. IRSCHIK to be completed in Summer 2007
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Model Set-up in GWK (1)Model Set-up in GWK (1)
5 inclinations of test cylindera = -45°/-22,5°/0°/22.5°/45°
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Model Set-up in GWK (2)Model Set-up in GWK (2)
Flume wall:
• current meters (8)propeller probes (4)Acoustic Doppler Velocimeters (ADV) (4)
• wave gauges (20)
Test cylinder:
• five inclinationsα = -45°/-22,5°/0°/22.5°/45°
• force transducers -strain gauges- (8)top and bottom bearinginline and transverse
• pressure transducers (16)front-line
• wave gauges (4)
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Wave Conditions Tested in GWKWave Conditions Tested in GWK
GWK-Datax= 201m GWK-Data
x= 201m
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Breaker TypeBreaker Type
Example 1: T = 4s (Plunging Breaker)
Example 2: T = 8s (Collapsing Breaker)
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collapsing breaker
breaker tongue at SWL
very small air gap
breaker tilt angle >45°
plunging breaker plunging breaker
breaker tongue at top
air gap
breaker tilt angle 30-45°
collapsing breaker
Breaker Tilt AngleBreaker Tilt Angle
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Breaker Tilt AnglesBreaker Tilt Angles
collapsing breaker
breaker tongue at SWL
very small air gap
breaker tilt angle >45°
plunging breaker
breaker tongue at top
air gap
breaker tilt angle 30-45°
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Breaking Wave Loads in Shallow WaterBreaking Wave Loads in Shallow Water
1 2
3 4
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Normalized Max Total ForceNormalized Max Total Force
0
0.5
1
1.5
2
2.5
F tot/ρ
gDH
zyl2
[ -
]
-8 -6 -4 -2 0 2 4distance xb-xcyl [m]
quasi-static load (constant)
Time Dependentimpact force
(highly variable)
3D model of Wienke(2001)
Morison equation
+
x = xb = Breaking Point Location:
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Curling FactorsCurling Factors
Curling factor
bbS
dyn
CR)t(C
)t(F
η⋅⋅⋅⋅ρ=λ 2
0
0.2
0.4
0.6
0.8
1
curli
ng fa
ctor
[-]
-6 -4 -2 0 2 4distance xb-xcyl [m]
Wiegel (1982)
The time history of the impact can be estimated using the same curling factors for both plunging and collapsing breakers
b
areaimpactofheightη
=λ
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Impact Force: Curling Factor lImpact Force: Curling Factor l
Estimation of curling factor λ for maximum loading caseCu
rling
–Fa
ctor
λ[-
]
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Impact Force: Curling Factor lImpact Force: Curling Factor l
Comparison with Goda et al. (1966), Wiegel (1982) and Wienke (2001)Wienke (2001): transient wave packets on horizontal bottom – “freak waves”
Mean of 10% highest values.
Curli
ng –
Fact
or λ
[-]
Wienke (2001)loading case 3(most critical)
Wienke, J (2001): Impact loading of slender pile structures induced by breaking waves in deeper water, PhD-Thesis, Leichtweiss-Institute, TU Braunschweig (in German)
Irschik, K. (2007): Impact loading of slender pile structures induced by depth limited breaking waves, PhD-Thesis, TU Braunschweig (in German)
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2.4 Effect of Neighbouring Piles on Wave Loading of Slender Pile
References:
• Sparboom, U; Hidelbrandt, A; Oumeraci, H. (2006): Group interaction effects of slender cylinders under wave attack. Proc. ICCE´06
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Measuring Cylinder in GWKMeasuring Cylinder in GWK
Model set-up in theLarge Wave ChannelCROSS - SECTION
5.00m
7.00
m
2.50
m
SWL+4.26m
0.00 m
+2.40m
3.00
m+
Support structure
Wave gauges
Straingauges
MeasuringcylinderD = 0.324m
Currentmeters
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Measuring Cylinders and Locations of Neighbouring CylindersMeasuring Cylinders and Locations of Neighbouring Cylinders
Model set-up in theLarge Wave ChannelPLAN VIEW
Wave gauges
107.29 m
106.64 m
105.99 m
104.69 m
104.04 m
103.39 m
102.74 m
102.09 m
105.34 m
Location in front of the wavemaker
Currentmeters
Video control
Video control
Measuring cylinder
2.50m
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Cylinder Group Configurations TestedCylinder Group Configurations Tested
Measuring cylinder
Neighbouring cylinder
D = Cylinder diameter
c = Incident wave direction
15 Investigated cylinder group configurations
see paper Sparboom, U.; Hildebrandt, A.; Oumeraci, H in Proc. ICCE ´06
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Loading Cases for the Selected Cylinder Group Configurations (1)Loading Cases for the Selected Cylinder Group Configurations (1)
Loading case 1
D
waves waves
D D
waves
3D3D
wavesCylinder configur-ations D
D
D D D
D D
Loading case 2
Loading case 3
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Loading Cases for the Selected Cylinder Group Configurations (2)Loading Cases for the Selected Cylinder Group Configurations (2)
Loading case 5
D
waves waves
D D
waves
3D3D
wavesCylinder configur-ations D
D
D D D
D D
Loading case 4
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Tested Wave ConditionsTested Wave Conditions
Water Depthd = 4.26 m
(a) Regular Non-Breaking Waves
(b) Irregular Non-Breaking Waves(JONSWAP)
(c) Breaking Waves(Gaussian Wave packets)
Water Depthd = 4.26 m
Water Depthd = 4.26 m
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Instrumented Cylinder with Two Lateral Cylinders (Video)Instrumented Cylinder with Two Lateral Cylinders (Video)
Instrumented Cylinder
DD
3D 3DD
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Surface elevation and wave height development in thenear field of a single isolated cylinder for loading cases 1-5Surface elevation and wave height development in thenear field of a single isolated cylinder for loading cases 1-5
WG 56
78
9
0
0,5
1
1,5
2
00,511,52t [s]
η [m]
SWL
loading case 1 loading case 2
loading case 3loading case 4
loading case 5
1,5
2,0
2,5
3,0
5 6 7 8 9 10 11 12 13
H [m]
cylin
der a
xis
0 1.3 m1.3 m 2.6 m2.6 m
wave gauge location
(a) Locations of wave gauges and cylinder
(b) Surface elevation above SWL
(c) Wave development in front and behind the cylinder
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Bending moments and surface elevation for isolated single cylinderBending moments and surface elevation for isolated single cylinder
My (t)
η (t) : surface elevation at cylinder location
Mx (t)
Mr (t)
Mx= Moment in longitudinal directionMy= Moment in transverse directionMr= Resulting MomentΔt= Phase lag related to ηmax
Regular Waves: H = 1.4m; T = 4s
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Measured wave kinematics with calculated accelerationsMeasured wave kinematics with calculated accelerations
u= horizontal Particle velocityv= vertical Particle velocity
Regular Waves: H = 1.4m; T = 4s
η(t) u(t)
du/dtdv/dt
v(t)
62
Bending moments and surface elevation for side-by-side arrangementBending moments and surface elevation for side-by-side arrangement
Regular Waves: H = 1.4m; T = 4s
My (t)
η (t)
Mx (t) Mr (t)
Mx= Moment in longitudinalMy= Moment in transverse directionMr= Resulting MomentΔt= Phase lag related to ηmax
: surface elevation at cylinder location
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Wave kinematics for side-by-side arrangementWave kinematics for side-by-side arrangement
Regular Waves: H = 1.4m; T = 4s
u= horizontal Particle velocityv= vertical Particle velocity
du/dtdv/dt
η(t) u(t)
v(t)
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Reduction Amplification Factor for Loading Cases 1-5 Reduction Amplification Factor for Loading Cases 1-5
Configuration no.2 Configuration no.7 Configuration no.12
LC 1 0,50 1,19 1,11LC 2 0,62 1,27 1,04LC 3 0,59 1,24 1,05LC 4 0,64 1,31 1,11LC 5 0,78 1,17 0,92
Coefficient C =
Mgroup
Msingle
[ ] D D
D
3D
3D
Reduction Amplification
Factor
= group
sin gle
MK
M
[-]
waves waves wavesD D
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3. Wave Forces on Submerged Bodies
References:
• Recio, J.; Oumeraci, H. (2006): Geotextile Sand Containers for Coastal Structures – Hydraulic Stability Formulae and Experimental Determination of Drag, Inertia and Lift Coefficients. Progress Report LWI (1st Draft), December 2006
66
Sliding and Overturning StabilitySliding and Overturning Stability
+⎡ ⎤⎣ ⎦≥∂
Δ −∂
D L2c(overt.)
M
0.05C 1.25Cl u
u0.5 g 0.1Ct
Overturning Formula
+ μ⎡ ⎤⎣ ⎦≥∂
μΔ −∂
D L2c(sliding)
M
0.5C 2.5Cl u
ug Ct
Sliding Formula( )= μ −Resisting GSC liftF F F
Resisting Force:Weight of GSC-Lift Force-Buoyancy
Horizontal Sliding
Mobilising force:Drag + Inertia force
Mobilising force:Drag + Inertia force
Resisting Force
∂+ = ρ + ρ
∂2
D M w D s M w
uF F 0.5 u C A C V
t
Resisting Moment
Mobilising force:Drag + Inertia force
Mobilising Moment >=Resisting Moment
≥ + +c c c cGSC D M L
l l l lF F F F
2 10 10 2Mobilising Moment:(Drag force + Inertia force) x
lc/10:
+c cD M
l lF F
10 10 cl10
Rotation Point 0
cl2
cGSC
lF
2
a) Overturning Stability
a) Sliding Stability b) Analysed condition
b) Analysed condition
Empirical Coefficients (CD, CM and CL) needed
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Tested Configurations (1)Tested Configurations (1)
68
Tested Configurations (2)Tested Configurations (2)
69
Tested Configurations (3)Tested Configurations (3)
70
Tested Configurations (4)Tested Configurations (4)
71
Reynolds Numbers and KC Numbers for Tested ConditionsReynolds Numbers and KC Numbers for Tested Conditions
72
Comparison Aceleration Data-Linear TheoryComparison Aceleration Data-Linear Theory
73
Comparison with COBRAS-ComputationsComparison with COBRAS-Computations
Horizontal Forces
Forc
es[N
]
Time [s]
z= 0.13m
Calc. CobrasMeasured
Difference within12%
seaw
ard
land
war
d
0 10 20 30
74
Drag DominanceDrag Dominance
Horizontal Velocity
Horizontal Force
75
Maximum Solitary Wave Generated in LWI-Twin Wave FlumeMaximum Solitary Wave Generated in LWI-Twin Wave Flume
76
Comparison of Solitary Wave Shape Measured with CobrasComparison of Solitary Wave Shape Measured with Cobras
(a) Free Surface experiment (b) Free Surface Cobras
110 115
77
4. Wave Loads on Monolithic Breakwaters and Sea Walls
78
4.1 Wave Loads Classification
79
Parameter Map for Classification of Loading CasesParameter Map for Classification of Loading Cases
Oumeraci et al (2001):Prohabilistic Design of Vertical Breakwaters. Balkema, Amsterdam 316 p.
α= = = = = +
hh B FH eq* * * * *b s bhwith h ; H ; B ; F and B Bs eqb h b2h h L 2tanρ g Hs s h bs
*sH35.0 <
Large wave
6.0*sH2.0 <<
Large wave
6.0*sH2.0 <<
Large wave
2.0*sH1.0 <<
Small wave
35.0*sH <
Small wave
6.0*sH >
Very large wave
2.0*sH1.0 <<
Small wave
2.0
6.0
8.0
0.1 0.20.0
0.0
4.0 Fhmax F hq
F h*
t/T
2.0
6.0
8.0
0.1 0.20.0
0.0
4.0 F hmax Fhq
Fh*
2. Slightly breaking wave 4. Broken waves
t/T
2.0
6.0
8.0
0.2 0.40.0
0.0
4.0Fhmax F hq
F h*
1. Quasi-standing wave
(quasi-static analysis) (quasi-static analysis) (dynamic analysis) (quasi-static dynamic/analysis)
0.1
q,hF
max,hF≈ 5.2
q,hF
max,hF0.1 <<
2.0
6.0
8.0
0.1 0.20.0
0.0
4.0
Fhmax
Fhq
Fh*
5.2
q,hF
max,hF>
t/T t/T
3. Impact loads
12.0*
B08.0 <<
Narrow berm
4.0*
B12.0 <<
Moderate berm
4.0*
B >
Wide berm
Composite breakwater
dhs
L
Hsi
hs
dhs
SWL SWL
Moderate mound
0.6 < hb < 0.9*
Low mound
0.3 < hb < 0.6*
Vertical breakwater
hb < 0.3*
Crown wall of rubble-mound breakwater
hb > 1.0*
SWLd
hshr
High mound
0.9 < hb < 1.0*
SWL
hrhb
Bb
Beqhb
hb
80
Characteristics of Pulsating and Impact Wave LoadsCharacteristics of Pulsating and Impact Wave Loads
SWL
a) quasi-static load (pulsating)
2h hF F / gH= ρ
t / T
hF
uFTN= natural period of
structure oscillation
h,max
d
d N
F 2,5
t 0,5
t T
<
≈
>
h,maxF
d dt t / T=
h,maxP
u,maxP h,max
u,max
P1,0
g HP
0,5g H
≈ρ ⋅ ⋅
≈ρ ⋅ ⋅
SWL
b) Impact load
2h h bF F / gH= ρ
t / T
h,maxP
u,maxP
hF
uF
h,max
d
d N
F 2,5 bis 15
t 0,01 bis 0,001
t T
=
≈
<
T= Wave period
h,max
b
u,max
b
P2 bis 50
g H
P2,0
g H
≈ρ ⋅ ⋅
≈ρ ⋅ ⋅
d dt t / T=
h,maxF
(*)
(*)
(*) Figures represent only order of magnitude
81
4.2 Breaking Wave Loads
82
Breaking Wave Loading of Caisson Breakwaters in GWKBreaking Wave Loading of Caisson Breakwaters in GWK
VerticalBreakwater
83
Breaking Wave Loads and Splash in GWK (Video)Breaking Wave Loads and Splash in GWK (Video)
84
Breaking Wave LoadsBreaking Wave Loads
Slightly breaking waves(pulsating load!)
Strongly breaking waves(impact load)
bH
h,maxFh,maxF
2h bF / gHρ 2
h bF / gHρ
t / Th,max
h,q
F1,0 2,5
F= ÷ h,max
h,q
F2,5
F>
GODA-Formulae(static stability analysis)
T = Wave period
PROVERBS-Approach(dynamic stability analysis)
h,qF
t / T
h,qF
FhFh
85
Simplified Force Time HistorySimplified Force Time History
t
tdFh
t rFh t
F h,max
rFhI rFhIdFhI
dFhI
F (t)h h
t d
t r
F (t)
Actual load Idealised load
86
t
Fh(t)
t d
t r
SWL
Fh,max
p3 = 0.45 p1
t
Fh (t)
p1
Fh,max
lFh
p4
SWL = Static Water Level
dc
= 0.8HbR = freeboardc
cR
d
h*
Simplified Impact Pressure Distribution (Parameterization)Simplified Impact Pressure Distribution (Parameterization)
87
Calculation of Static Equivalent Wave Loads (1)Calculation of Static Equivalent Wave Loads (1)
( )h D h,maxstatF F= ν ⋅
Calculation of dynamic load factor νD by assuming a triangular load-time function:
with νD = dynamic load factor
For more details see Oumeraci, H. (2004): „Caisson breakwaters“ in Planning and Design of Ports and Marine Terminals, pp. 155-262 2nd Edition by H. Agerschou, Thomas Telford, London.
(1)
•Rise time of Impact force tr:
2
2A w s
h,max
hg
t g H4F
π ⋅= ρ ⋅ ⋅ ⋅
• Total load duration td:
⎡ ⎤⎛ ⎞= ⋅ + ⋅ −⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
Ad A
p
tt t 2.0 8 exp 18
T
or approximated by: ≈d At 2.5 t
h = Water depthdirectly at thewall
(3)
(4)
(5)
Tp = PeakPeriode
• Maximum Impact force Fh,max[kN/m]:
2h,max w bF 10 g H≈ ρ ⋅ ⋅ Hb = Breaker height(2)
−
ν
⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥ν = + π⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦⎣ ⎦
⎛ ⎞= ⎜ ⎟
⎝ ⎠
D
0,55
d dD
N N
0,63
d
A
Dynamic load factor
t t1.4 tanh 0.25 2 c
T T
twith c 0.55
t
(6)
h,maxF
Timetrtd
88
Calculation of static Equivalent Wave Loads (2)Calculation of static Equivalent Wave Loads (2)
stat,equ D dyn,maxF F= ν ⋅
d
A
tk
t=
d Nt / T −⎡ ⎤⎣ ⎦
dyn
amic
load
fact
orν D
[-]
relative Load Duration
Ns
MT 2
K≈ π
Natural Period:
M=Mass, Ks= Stiffness
tA tEtd
3.0
−
ν
⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎢ ⎥ν = + π =⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦⎣ ⎦
D
0,55 0,63
d d dD
N N A
Dynamic load factor
t t t1.4 tanh 0.25 2 c with c 0.55
T T t(6)
89
±0,0
Fh
Effect of Successive Breaking Wave LoadsEffect of Successive Breaking Wave Loads
(a) Horizontal breaking waveforce
(b) Accumulation of residual displacement
(c) Caisson displacements
horiz. Force Fh [kN/m]
Time [s]
Total horiz. Displacement of Structure [cm]
Time [s]
90
SAKATA-Habour (Japan)SAKATA-Habour (Japan)
14.5m
hc=11.63m-3.43m
d
B=17.0m
-9.00m
±0.00
Storm surge (1973/74):Hmax: ≈10.0m (tD=0.6s)TP : 13.0s
Static Standard Approach: Dynamic calculation (tD=0.6s):
Caisson dimensions:Width: B=17.0mHeight : hc=11.63mLength: L=20.95m
ηS= Safety coefficient against sliding
ηS=1.2 ηS=0.50
91
Breaking Wave Impact on SAKATA BreakwaterBreaking Wave Impact on SAKATA Breakwater
Storm surge im Winter 73/74 ⇒ Hmax=10m, Tp=13s Credit: Dr. Takahashi, PARI
92
Sliding of Caisson in SAKATA-Harbour in the Storm Surge1973/74Sliding of Caisson in SAKATA-Harbour in the Storm Surge1973/74
B=17m; h=11-12m; L≈21m ⇒ Hs≈7m; T=13s
Although safety coefficient against sliding ηs=1.2 and against tilting ηov>5 according to static (Standard) approach.
Credit: Dr. Takahashi, PARI
93
Dynamic Stability Calculation of SAKATA BreakwaterDynamic Stability Calculation of SAKATA Breakwater
Impact load forHmax=10m, Tp=13s and d=3.43m
Adhesion and frictionforce
Horizontal displacementof Caisson: ca. 20mm/Impact event
Caisson-Length: L≈21m
HS= 6.9mTp= 13.0sd = 3.43m
14.5m
hc=11.63m-3.43m d
B=17.0m
-9.00m
±0,00
94
Seaward Impact Loading Induced by Wave OvertoppingSeaward Impact Loading Induced by Wave Overtopping
Seaside
Uplift
Harbour side
Seaward impactpressure
Fh, sea
SWL
Overtopping plume
Entrapped air
Schüttrumpf, A. (2006): Uplift force on monolithic structures induced by breaking waves and under overtopping conditions – PhD-Thesis, TU Braunschweig (1st Draft)
95
Research Performed in PROVERBS for Wave Impact of VerticalStructuresResearch Performed in PROVERBS for Wave Impact of VerticalStructures
Parameter Mapfor classification of loading case
Berm heightand width
Water depth &wave conditions
at structure
IMPACT LOADING
h,1F
u,1F
F s,2
1 22
F u,2
F v,2
Slamming on topslab Fv,2
outside Proverbs
Effect of waveovertopping
Seaward impactloads Fs,2
see Section 2.5.2
Vertical Loads(uplift)
New prediction methodswith following steps:
* pressure distribution
* correction of Ffor aeration
* force historyF = f (duration)
* statistical distributionof max. force (F )
u,1
u,1
u,1
Constructional Measures to Reduce Impact Forces
* Rubble as Damping Layer (Section 2.8.2)* Perforated Structures (Section 2.8.1)
* Unconventional Alternatives Related to Front Geometry (MCS-Project) and foundation (Section 3)
Horizontal Loads(shoreward)
New prediction methodswith following steps:
* pressure distribution
* correction of Ffor aeration
* force historyF = f (duration)
* statistical distributionof max. force (F )
h,1
h,1
h,1
(Oumeraci et al, 2001)
96
4.3 Scale Effects Associated with Breaking Wave Impacts
97
Physical Processes Involved in the Wave Load History and Associated scaling ProblemsPhysical Processes Involved in the Wave Load History and Associated scaling Problems
Time t
Compression of AirPocket
Impact of BreakerTongue
Oscillations of AirPocket
Escape of AirMaximal Run-up
FROUDE
FROUDE MACH-CAUCHY
AND FROUDE
MACH-CAUCHY
MACH-CAUCHYAND FROUDE
F = N Fh, nature h, modelLt = N tnature modelL
αF
αt
C FROUDE: α = 3 and α = 0.5C MACH-CAUCHY: α = 2 and α = 1.0
C ALTERNATIVE Scaling depending on air entrainment: α = 2 to 3 α = 0.5 to 1.0 t
ttF
F
F
(Oumeraci & Hewson, 1997)
98
Suggested Procedure for Scaling the Various Components of the Wave Load HistorySuggested Procedure for Scaling the Various Components of the Wave Load History
quasi-static compon
F (Froude)q
Time t
F (t) impact component governed by compressibility
governed by gravity
F (MACH- Cauchy)dyn
oscillatory component
F (Mach-Cauchy)osc
governed by compressibility
Cauchy: t rt di
t dt q
Froude:Cauchy - Froude:
Froude:
scaling of total force history:
F (t) =tot (F ) + (F ) + (F )dyn oscMACH-Cauchy
Froude[ ]
(Oumeraci et al, 2001)
99
Scale Effects in Modelling Breaking Wave Loading and Response of Sea DikesScale Effects in Modelling Breaking Wave Loading and Response of Sea Dikes
SurfaceCAUCHY
( REYNOLDS )
Breaker and Impact
WEBERREYNOLDSCAUCHY
C
Run-up and down
REYNOLDS( WEBER )
Bottom friction
REYNOLDSCore material
CAUCHY
WaveFROUDE
(after Führböter, 1986)
1:1 1:10 1:100
Gravity
Friction
Elasticity
SurfaceTension
FROUDE
REYNOLDS
CAUCHY
WEBER
1
1
1
1 1:100
1:10
1:31.6
1 1
1:1000
1:100
1:10000
Force ScaleModelLaw
100
4.4 Broken Wave Loads on Sea Walls
101
(a) Seawall front landwardof shoreline
Broken Wave Loads: Load Cases According to SPM (1984)Broken Wave Loads: Load Cases According to SPM (1984)
(b) Seawall seawardof shoreline
SWL
SeawallFront of seawall
Beach slope
Shoreline
Virtual max. run-up
SWL
Front of seawallSeawall
Shoreline
Broken wave
Broken wave
102
Assumption According to CEM (2003)Assumption According to CEM (2003)
α
bh
BH bH ´
(Breaking depth)
Beach slope 1:m
wh
SWL
Bore height
Bore velocity
b bH ´ 0,78 H= ⋅
b b bv c g h= = ⋅
ww1 b
b
hH 0,2 0,58 H
h⎛ ⎞
= + ⋅ ⋅⎜ ⎟⎝ ⎠
w1 b bv c g h= = ⋅
RWS bH 0,2 H= ⋅
RWS b bv c g h= = ⋅
2w2 b
A
xH 0,2 H 1
x⎛ ⎞
= ⋅ −⎜ ⎟⎝ ⎠
2w2 b b
A
xv c g h 1
x⎛ ⎞
= = ⋅ ⋅ −⎜ ⎟⎝ ⎠
w1HSWLH
1 2
w2H
Linear decrease of bore heightmax. run-up
Av 0=A
( )A maxz
(shoreline)U
α
2x
( )A A maxx z / tan= α
linear decrease of bore velocity from
at max. run-up
= ⋅ =SWL b Av g h to v 0
linear decrease of bore height
1
2
Seawall front seawards of shoreline
Seawall front landwards of shoreline
Breaker height
bc bc bc
(1) (2) (3) (4)
(5) (6) (7) (8)
103
Seawall Front Seawards of Shoreline: Wave Load FormulaeSeawall Front Seawards of Shoreline: Wave Load Formulae
SWL
α
1
Wave pressure
Fstau
shorelineU
wh
ww1 b
b
hH 0,2 0,58 H
h⎛ ⎞
= + ⋅ ⋅⎜ ⎟⎝ ⎠
2wo w1
1F g H ;
2= ⋅ ρ ⋅ ⋅
wu w1 wF g H h ;= ρ ⋅ ⋅ ⋅
2
stauv
p2
= ρ ⋅
w w1p g H= ρ ⋅ ⋅
bv g h= ⋅
= ⋅SWL bH 0,2 H
hydrostatic pressure
stat w1p g h= ρ ⋅ ⋅ w w1p g H= ρ ⋅ ⋅
hb = Breaking depth
Hb = Breaker height for water depth hb
Force Components:
stau b w11
F g h H2
= ⋅ ρ ⋅ ⋅ ⋅
2stat w1
1F g H
2= ⋅ ρ ⋅ ⋅
Fwo
Fstat
Fwu
104
Seawall front landwards of shoreline: Wave Loads FormulaeSeawall front landwards of shoreline: Wave Loads Formulae
SWL
2
(maximum run-up)A
2w2
stau
vp
2= ρ ⋅
w w2p g H= ρ ⋅ ⋅
2w2 b
A
xv g h 1
x⎛ ⎞
= ⋅ ⋅ −⎜ ⎟⎝ ⎠
Fwo
Fstau
= ⋅SWL bH 0,2 H
U (shoreline)2xα
2w2 b
A
xH 0,2 H 1
x⎛ ⎞
= ⋅ ⋅ −⎜ ⎟⎝ ⎠
HSWL = Bore height at shoreline Hw2 = Bore height at wall
zA
2wo w2
1F g H
2= ⋅ ρ ⋅ ⋅
2stau b w2
A
x1F g h H 1
2 x⎛ ⎞
= ⋅ ρ ⋅ ⋅ ⋅ ⋅ −⎜ ⎟⎝ ⎠
A Ax z / tan= α
zA= max. wave run-upSee also PhD-Thesis RAMSDEN (Caltech).
105
4.5 Wave Force Reduction by Armouring (Tests Performed in Large Wave
Flume)
106
Wave Force Reduction by ArmouringWave Force Reduction by Armouring
h
h
h Bb
Caisson
DWL
H
d0 sd
B bottom
B
hr
Sandd sand
b0 c
b
b
DWL Rc
B crownTetrapodlayer
x
1 Definition of parameters:• DWL = design water level• Bcrown = crest width (larger than two armour blocks)• m = cot α = 1.35 to 1.50• Rc = freeboard• Lhs = wave length for depth hs at toe• b0 = width of dissipating mound at height of DWL
+= +
+bottom crown
0 crown ss c
B Bb B h
h R
107
Damping of Pulsating Wave Loads by ArmouringDamping of Pulsating Wave Loads by Armouring
0 0.5 1 1.5 2 2.5 3 3.5 4
Time t [s]
without dissipating mound
(μD,h)max
(Fh)max = 1.2
(Fh)max = 0.6
0 0.5 1 1.5 2 2.5 3 3.5 4
Time t [s]
without dissipating mound
with dissipating mound
(Fu)max = 0.9
(Fu)max = 0.5
(μD,u)max
μD,h=Fh -Fh,D
Fh
μD,u=Fu -Fu,D
Fu
(Oumeraci, 2004)
≈ 50%
≈ 40%
with dissipating mound
with dissipating mound
with dissipating mound
108
Damping of Pulsating Wave Loads by ArmouringDamping of Pulsating Wave Loads by Armouring
30 0.5 1 1.5 2 2.5 4
Time t [s]
with dissipating mound
without dissipating mound
= 4.1
= 0.9
3.53.53.5
Fh max( )
μ D,h =Fh -F h,D
Fh
Fh max( )
(μD,h)max
0 0.5 1 1.5 2 2.5 3 3.5 4
Time t [s]
without dissipating mound
with dissipating mound
(μD,u)max
(Fu)max = 2.6
(Fu)max = 0.7
μD,u=Fu -Fu,D
Fu
(Oumeraci, 2004)
≈ 80%≈ 60%
with dissipating mound with dissipating mound
109
4.6 Stability of Structure Foundation Under Extreme Wave Loads
110
Main Modes of Vertical Breakwater FailureMain Modes of Vertical Breakwater Failure
OVERALL FAILURE MODES
a) Sliding b) Overturning
c) Settlement followed by slipfailure and seaward tilt
d) Settlement followed by slipfailure and shoreward tilt
SWL SWL
SWLSWL
W'
Fh
F vμ (W' - F )v
W'
F h
Fv
lh
lv
F 'h
F 'v
W'
Fv
F h
W'
LOCAL FAILURE MODES
f) Punching failure at seaward andshoreward edges
e) Erosion beneath seaward andshoreward edges
g) Seabed scour and toe erosion
SWLSWL
SWL
Erosion ofrubble mound toeScour hole
A B
111
Wave Induced Dynamic Process in Foundation of Coastal StructuresWave Induced Dynamic Process in Foundation of Coastal Structures
Measuring Devices:
0.00 m Flume Bottom
2.45 m
3.45 m
7.00 m Wave Flume (Top Level)
1:1.5
4.05 m SWL
3.30 m
2.76
m
2.50 m
1.00
m
7.20 m
Sand D50 = 0.21 mm
Impermeable Sheets
CaissonwithSandfill
Sand D50 = 0.35 mm
Sand D50 = 0.35 mm
Separation Wall (Sandbags)
HS, TP
4.05 m SWL
Sand BermD50 = 0.35 mm
Bedding layer 0.2 mSand layer 2.45 m
Pressure1
1 1
1
11111
1
1 1
Wave GaugesInductive Displacement
Meters
Pore Water Pressure2
2 2 2 2 2 2 2
2 2 2 2
2 2 2
2 2 2 2
Pore Water Pressure + Total Stress (isotropic)3
3 3
3 3Electrical ConductivityMeasurement
112
Caisson Breakwater Construction in GWKCaisson Breakwater Construction in GWK
113
Loading cycles [-]
-60
-40
-20
0
d v,b [
mm
]
0
5
10
u r [
kPa
]
-5
0
5
10
u t [
kPa
]
-3
-2
-1
0
d v,b [
mm
]0
100
200
300
Mt
[ kN
m/m
]
Processes Leading to Partial Soil LiquefactionProcesses Leading to Partial Soil Liquefaction
Regular waves: H=0.9m, T=6.5s, hs=1.6m
(d)Residual pore pressure (P36)
(e)Residual deformation (vertical)
0S ≈ 373 cycles
692Number of wave load cycles [-]
Mean Value Mt,max ≈ 210 kNm/m
(c)Transient pore pressure (P36)
(b)Transient motions of theshoreward caisson edge
(a)Total moment around caisson heel
dv,b
-P36
III
S
hs Mt
114
-10
-8
-6
-4
-2
0
d v,b
[ m
m ]
-3.5
-3.0
-2.5
Wave-Induced Pore Pressure and Soil Deformation BenesthStructures (Soil Liquefaction)Wave-Induced Pore Pressure and Soil Deformation BenesthStructures (Soil Liquefaction)
Regular waves with H=0.7m, T=6.5s, hs=1.6m
Zoom
Δdv,b=0.3 mm
dv,b
-P36
III
(a) Vertical caisson motion dv,b (t)
Residual
Transient
100 200 300 400 500 600 700 800 900 1000Time [ s ]
0
1
2
3
4
5
u [
kPa
]
123
(b) Pore pressure response u(t) under the shoreward edge of the caisson (P36)
Δur=0.2 kPaZoom
S
Residual
Transient
Residual pore pressure
Transient pore pressure
S≈54 cycles
hs
115
-2.0 -1.5 -1.0 -0.5 0.0Downward motion
amplitude dv,b [mm]
0
1
2
3
4
Resid
ual p
ore
pres
sure
ur
[kPa
]af
ter 5
3 lo
adin
g cy
cles
Dr≈0.31Dr≈0.31Dr≈0.35Dr≈0.35Dr≈0.40Dr≈0.40
Residual Pore Pressure vs. Caisson MotionsResidual Pore Pressure vs. Caisson Motions
(dv,b)crit= -0.3mm
PulsatingLoad
ImpactLoad
-
P36
III
Dr ≈ 0.31
Dr ≈ 0.35
Dr ≈ 0.40
dv,bhs
123
Thank you for your attention!